US9860097B2 - Transmitting device, receiving device, and transmitting and receiving system - Google Patents

Transmitting device, receiving device, and transmitting and receiving system Download PDF

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US9860097B2
US9860097B2 US14/976,823 US201514976823A US9860097B2 US 9860097 B2 US9860097 B2 US 9860097B2 US 201514976823 A US201514976823 A US 201514976823A US 9860097 B2 US9860097 B2 US 9860097B2
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digital signal
transmitting
specific frequency
frequency component
compressed
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US20160112227A1 (en
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Haruki Kawakami
Tohru Asami
Yoshihiro Kawahara
Masami Kishiro
Takahiro Kudo
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Fuji Electric Co Ltd
University of Tokyo NUC
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Fuji Electric Co Ltd
University of Tokyo NUC
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
    • H04L27/22—Demodulator circuits; Receiver circuits
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/145—Square transforms, e.g. Hadamard, Walsh, Haar, Hough, Slant transforms
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
    • H03M7/3062—Compressive sampling or sensing
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3068—Precoding preceding compression, e.g. Burrows-Wheeler transformation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/02—Transmitters
    • H04B1/04—Circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/12—Arrangements for detecting or preventing errors in the information received by using return channel
    • H04L1/16—Arrangements for detecting or preventing errors in the information received by using return channel in which the return channel carries supervisory signals, e.g. repetition request signals
    • H04L1/18—Automatic repetition systems, e.g. Van Duuren systems
    • H04L1/1867—Arrangements specially adapted for the transmitter end
    • H04L1/1887—Scheduling and prioritising arrangements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32154—Transform domain methods
    • H04N1/32176—Transform domain methods using Walsh, Hadamard or Walsh-Hadamard transforms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/0007—Code type
    • H04J13/004—Orthogonal
    • H04J13/0048—Walsh

Definitions

  • the disclosure relates to a transmitting device, a receiving device, and a transmitting and receiving system, which enable accurate decompression even if the original input digital signal has low sparsity.
  • wireless sensor nodes for which low power consumption is demanded, reducing the wireless transmission power, which largely accounts for the power consumption, is indispensable.
  • One of techniques therefor is reducing the wireless transmission power by reducing the amount of data by data compression of transmission data.
  • compression techniques such as of ZIP and LZH
  • Data compression by these compression techniques requires many arithmetic operations, and thus is not suitable for implementation on wireless sensor nodes, for which low power consumption is demanded. For example, if such data compression is applied to a wireless sensor node, power consumed by compression operations may become greater than the amount of reduction in the wireless transmission power and the overall power consumption may actually be increased.
  • Compressive sensing is a technique that allows data compression with low power consumption.
  • Compressive sensing is described in detail in, for example, “Implementation of Compressive Sensing on Sensor Node by Use of Circulation Matrix and Evaluation of Power Consumption”, by Tatsuya Sasaki, IPSJ SIG Technical Report 2012 (hereinafter, referred to as Sasaki document).
  • this compressive sensing is a technique for accurately executing decompression into the original signal, from data that have been compressed to a small number of data, by utilizing signal sparsity, which many signals in nature are said to have.
  • N the number of original data
  • M the number of data that have been compressed as a result of compression operations
  • N>M is satisfied, naturally.
  • the original data are represented by an input digital signal x, which is an N-dimensional vector
  • the data after compression are represented by a compressed digital signal d, which is an M-dimensional vector
  • the compressed digital signal d is able to be found by multiplying the input digital signal x by an observation matrix ⁇ of M rows and N columns.
  • d ⁇ x (1)
  • the original input digital signal x needs to have sparsity.
  • the original input digital signal x is able to be accurately decompressed.
  • a transmitting device includes: a compressing unit configured to generate and output a compressed digital signal that has been compressed, by converting an input digital signal by use of a Walsh function and extracting a specific frequency component.
  • a receiving device includes: a decompressing unit configured to decompress a compressed digital signal, which has been compressed by being converted by use of a Walsh function and a specific frequency component being extracted, into a transmission side input digital signal, by using an observation matrix corresponding to a Walsh function of the specific frequency component.
  • a transmitting and receiving system includes: a transmitting device, having: a compressing unit configured to generate and output a compressed digital signal that has been compressed, by converting an input digital signal by use of a Walsh function and extracting a specific frequency component; and a transmitting unit configured to wirelessly transmit and output the compressed digital signal; and a receiving device, having: a receiving unit configured to receive the compressed digital signal wirelessly transmitted and output by the transmitting unit; and a decompressing unit configured to decompress the compressed digital signal received by the receiving unit into the input digital signal by using an observation matrix corresponding to a Walsh function of the specific frequency component.
  • a transmitting and receiving system includes: a transmitting device, having: a first compressing unit configured to generate and output a first compressed digital signal that has been compressed, by converting an input digital signal by use of a Walsh function and extracting a specific frequency component; a second compressing unit configured to generate and output a second compressed digital signal that has been compressed, by converting an input digital signal with an observation matrix that uses a random matrix; a transmission side switch over unit configured to switch over, based on a switch over instruction signal, between processes by the first compressing unit and the second compressing unit; and a transmitting unit configured to wirelessly transmit and output the first compressed digital signal or the second compressed digital signal that has been output by the switch over by the transmission side switch over unit; and a receiving device, having: a receiving unit configured to receive the first compressed digital signal or the second compressed digital signal that has been wirelessly transmitted and output by the transmitting unit; a first decompressing unit configured to decompress the first compressed digital signal into the input digital signal by using an observation matrix corresponding to
  • FIG. 1 is a block diagram illustrating an overall configuration of a transmitting and receiving system, which is a first embodiment of this invention
  • FIG. 2 is a flow chart illustrating an outline of a transmission procedure by a transmitting device of the first embodiment
  • FIG. 3 is a flow chart illustrating an outline of a reception procedure by a receiving device of the first embodiment
  • FIG. 4 is a time chart schematically illustrating an outline of specific signal processing in the first embodiment of this invention.
  • FIG. 5 is a diagram of a vector representation of an input digital signal
  • FIG. 6 is a diagram illustrating a matrix used in compression or decompression by a compressing unit and a decompressing unit in the first embodiment
  • FIG. 7 is a diagram of a vector representation of a compressed digital signal
  • FIG. 8 is a diagram of a matrix representation of a basis transformation matrix used in a decompression process of the decompressing unit in the first embodiment
  • FIG. 9 is a diagram illustrating a relation between a 2 n -th order Hadamard matrix H(2 n ) and a 2 n+1 -th order Hadamard matrix H(2 n+1 );
  • FIG. 10 is a diagram illustrating generation of Hadamard matrices of up to 2 3 -th order specifically expressed with numerical values, based on the relation illustrated in FIG. 9 ;
  • FIG. 11 is a diagram illustrating a relation between a 2 3 -th order Hadamard matrix and a Walsh function corresponding to this Hadamard matrix
  • FIG. 12 is a diagram schematically illustrating a state of generating an extracted observation matrix extracting a specific frequency component, from an observation matrix corresponding to a Walsh function;
  • FIG. 13 is a power spectra diagram of vibration of an expressway elevated bridge, before compression and after decompression, when conventional compressive sensing using a random matrix as an observation matrix is applied;
  • FIG. 14 illustrates a power spectra diagram for a case where an input digital signal of vibration of the same expressway elevated bridge as that of FIG. 13 is compressed and decompressed by use of an extracted observation matrix corresponding to a Walsh function according to this first embodiment.
  • the upper figure ( FIG. 14( a ) ) is a power spectrum of the original input digital signal before the compression
  • the middle figure ( FIG. 14( b ) ) is a power spectrum for a case where decompression is executed by inverse Walsh transform, as will be described later
  • the lower figure ( FIG. 14( c ) ) is a power spectrum for a case where decompression is executed by use of the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform described later;
  • FIG. 15 is a diagram illustrating the basis transformation matrix corresponding to the inverse discrete Fourier transform
  • FIG. 16 is a block diagram illustrating a configuration of a compressing unit of a transmitting and receiving system of a second embodiment of this invention.
  • FIG. 17 is a block diagram illustrating a configuration of a decompressing unit of the transmitting and receiving system of the second embodiment of this invention.
  • FIG. 18 is a diagram illustrating a signal flow of fast Walsh-Hadamard transform algorithm
  • FIG. 19 is a diagram illustrating a specific example of fast Walsh-Hadamard transform
  • FIG. 20 is an explanatory diagram schematically illustrating an extraction process by a specific frequency component extracting unit
  • FIG. 21 is a diagram illustrating an example of extraction data specifying a specific frequency desired to be extracted
  • FIG. 22 is a diagram illustrating an example of rearrangement data held by a rearranging unit
  • FIG. 23 is a flow chart illustrating a transmission procedure of a transmitting device according to the second embodiment
  • FIG. 24 is a flow chart illustrating a reception procedure of a receiving device according to the second embodiment
  • FIG. 25 is a block diagram illustrating a schematic configuration of a transmitting and receiving system of a third embodiment of this invention.
  • FIG. 26 is a block diagram illustrating a detailed configuration of a compressing unit according to the third embodiment.
  • FIG. 27 is a block diagram illustrating a detailed configuration of a decompressing unit according to the third embodiment.
  • FIG. 28 is a flow chart illustrating a transmission procedure of a transmitting device according to the third embodiment.
  • FIG. 29 is a flow chart illustrating a reception procedure of a receiving device according to the third embodiment.
  • FIG. 30 is a block diagram illustrating a detailed configuration of a compressing unit according to a modification of the third embodiment.
  • FIG. 31 is a block diagram illustrating a detailed configuration of a decompressing unit according to the modification of the third embodiment.
  • FIG. 1 is a block diagram illustrating an overall configuration of a transmitting and receiving system, which is a first embodiment of this invention.
  • an accelerometer not illustrated measures an acceleration component of vibration of a structure
  • input digital signals x that have been converted into digital signals by an analog-digital converter not illustrated are respectively input to plural transmitting devices 1 corresponding thereto.
  • a compressing unit 11 generates a compressed digital signal d by compressing the input digital signal x
  • a transmitting unit 13 transmits this compressed digital signal d to a receiving device 2 side.
  • a receiving unit 21 receives the compressed digital signal d transmitted from the transmitting device 1 , and a decompressing unit 22 decompresses this compressed digital signal d and outputs it as a decompressed digital signal x′.
  • the receiving device 2 receives and decompresses plural compressed digital signals d transmitted from the respective transmitting devices 1 , but herein, reception and decompression of a compressed digital signal d transmitted from one transmitting device 1 will be described.
  • FIG. 2 is a flow chart illustrating an outline of a transmission procedure by the transmitting device 1 .
  • FIG. 3 is a flow chart illustrating an outline of a reception procedure by the receiving device 2 .
  • an input digital signal x is input to the transmitting device 1 .
  • This input digital signal is divided into compressive sensing frames, and a single compressive sensing frame corresponds to a single input digital signal x.
  • the input digital signal x is formed of a column of N data.
  • the compressing unit 11 generates and outputs a compressed digital signal d that has been compressed, by converting the input digital signal x by using a Walsh function and extracting a specific frequency component therefrom (Step S 101 ).
  • This extraction of a specific frequency component means selectively picking out a specific frequency component.
  • This specific frequency component is, for example, a signal component of a specific frequency domain including a natural frequency in monitoring of the natural frequency of a structure, or the like.
  • the compressing unit 11 converts an input digital signal x by using an observation matrix ⁇ a (hereinafter, referred to as an extracted observation matrix ⁇ a) corresponding to a Walsh function of a specific frequency component, and generates and outputs this converted digital signal as a compressed digital signal d.
  • the compressed digital signal d has been compressed into a column of M (M ⁇ N) data.
  • the transmitting unit 13 wirelessly transmits the generated compressed digital signal d (Step S 102 ). Since the relation M ⁇ N holds, the transmitting device 1 wirelessly transmits M data, which are less than the N data wirelessly transmitted, and thus power consumption in the wireless transmission is able to be reduced.
  • the receiving unit 21 receives the compressed digital signal d transmitted from the transmitting device 1 (Step S 201 ). Thereafter, the decompressing unit 22 executes a decompression process by using the extracted observation matrix ⁇ a and a basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform, by use of, for example, L1-norm minimization or the like, and generates and outputs a decompressed digital signal x′ (Step S 202 ).
  • the decompressed digital signal x′ is decompressed as N data, which are the same as the original input digital signal x, but has a decompression error, as will be described later.
  • This decompression error is dependent on sparsity of the input digital signal x if conventional compressive sensing is used, and the decompression error becomes small when the sparsity is high and the decompression error becomes large when the sparsity is low.
  • a transmitting and receiving system such as a wireless sensing system
  • the transmitting device 1 side which is a wireless sensor node that executes a compression process
  • power consumption needs to be reduced with battery drive or the like
  • a receiving device 2 side which executes a decompression process, is configured to be able to be sufficiently supplied with power
  • a compressive sensing technique that reduces the power consumption in the transmitting device 1 can be said to be suitable for the wireless sensing system.
  • FIG. 4 is a time chart schematically illustrating an outline of specific signal processing in the first embodiment.
  • a decompression process is executed by the decompressing unit 22 on the receiving device 2 side, and N decompressed digital signals x′, as many as those before the compression, are generated.
  • M ⁇ N wireless transmission power on the transmitting device 1 side is reduced.
  • FIG. 5 is a vector representation of the input digital signal x.
  • the input digital signal x is represented as a column vector having the number of elements of N.
  • FIG. 6 illustrates the extracted observation matrix ⁇ a used in the compression or decompression by the compressing unit 11 and the decompressing unit 22 .
  • the extracted observation matrix ⁇ a is expressed as a matrix of M rows and N columns.
  • FIG. 7 is a vector representation of the compressed digital signal d.
  • the compressed digital signal d is represented as a column vector having the number of elements of M, satisfying the relation, M ⁇ N.
  • Equation (3) Data compression in the compressive sensing according to this first embodiment is implemented by a matrix operation expressed by Equation (3).
  • FIG. 8 illustrates a matrix representation of the basis transformation matrix ⁇ used in the decompression process of the decompressing unit 22 .
  • the basis transformation matrix ⁇ is expressed as a matrix of N rows and N columns, and as will be described later, the decompressing unit 22 uses the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform.
  • the compressing unit 11 has an extracted observation matrix multiplying unit 12 .
  • the extracted observation matrix multiplying unit 12 multiplies the input digital signal x, which is a column of N data, by the extracted observation matrix ⁇ a (matrix product operation) as expressed by Equation (3) and generates the compressed digital signal d, which is a column of M data. Therefore, the number of operations by the extracted observation matrix multiplying unit 12 becomes M ⁇ N.
  • the observation matrix ⁇ in the conventional compressive sensing uses, as described in the Sasaki document, a random matrix, in which each element is random, but in this first embodiment, compression is executed by converting the input digital signal x by use of the extracted observation matrix ⁇ a corresponding to the Walsh function of the specific frequency component.
  • a Walsh function is a square wave function, in which a closed interval [0, 1] is equally divided into 2 n , and a value of each interval is +1 or ⁇ 1.
  • the Walsh function is a complete orthonormal function system having characteristics similar to those of a trigonometric function, and is able to execute Walsh series expansion of an arbitrary waveform having a cycle, similarly to Fourier series expansion.
  • the Walsh function is obtained by rearranging a Hadamard matrix.
  • the Hadamard matrix is a square matrix, which is formed of two values of ⁇ 1 and has a size of 2 n ⁇ 2 n , and when a 2 n -th order Hadamard matrix H(2 n ) is given, a 2 n+1 -th order Hadamard matrix H(2 n+1 ) is expressed as illustrated in FIG. 9 .
  • a Walsh function is obtained by rearranging series of respective rows of the Hadamard matrix H(2 n ) in order of their numbers of intersections.
  • the number of intersections is the number of times the values in the series of each row change from +1 to ⁇ 1, or from ⁇ 1 to +1.
  • rows In the Walsh function, in ascending order of the numbers of intersections, rows generally corresponding to a sin wave and a cos wave of Fourier series appear, and frequency corresponding thereto is increased.
  • the first row corresponds to direct current.
  • FIG. 11 illustrates a 2 3 -th order Hadamard matrix, and a Walsh function (waveform wal(k, t/T), where k is the number of intersections) corresponding to this Hadamard matrix.
  • a 2 8 -th order Walsh function not illustrated is used.
  • FIG. 12 is a diagram schematically illustrating a method of generating the extracted observation matrix ⁇ a extracting a specific frequency component from the observation matrix ⁇ corresponding to the Walsh function.
  • the specific frequency component is set around a natural frequency of a structure for health monitoring of the structure, for example. In this first embodiment, since the natural frequency of the structure is at around 4 Hz, the specific frequency component is set at 2 Hz to 5 Hz.
  • FIG. 13 illustrates power spectra of vibration (acceleration) of an expressway elevated bridge, before compression and after decompression, when conventional compressive sensing using a random matrix as an observation matrix is applied. That is, in FIG. 13 , the horizontal axis represents the frequency, and the vertical axis represents the power spectral density (PSD). The sampling frequency of the analog/digital conversion is 20 Hz, the upper figure ( FIG. 13( a ) ) illustrates the power spectrum of the original data before the compression, and the lower figure ( FIG. 13( b ) ) illustrates the power spectrum after the decompression.
  • This example is an example of a case where sparsity of the original input digital signal x is low, and on each of both sides of 4 Hz, the natural frequency of the elevated bridge, for example, a comparatively large peak is present.
  • the peak at 4 Hz the natural frequency that needs to be decompressed, has become small and the peaks on both sides thereof have been emphasized.
  • the decompression error is increased.
  • FIG. 14 illustrates power spectra in a case where an input digital signal x of vibration (acceleration) of the same expressway elevated bridge is compressed and decompressed by use of the extracted observation matrix ⁇ a corresponding to the Walsh function according to this first embodiment.
  • the sampling frequency of the analog/digital conversion is 20 Hz
  • the upper figure ( FIG. 14( a ) ) is a power spectrum of the original input digital signal x before the compression
  • the middle figure FIG. 14( b )
  • FIG. 14( b ) is a power spectrum for a case where decompression is executed by inverse Walsh transform, as will be described later
  • the lower figure FIG.
  • FIG. 14( c ) is a power spectrum for a case where decompression is executed by use of the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform described later.
  • the original input digital signal x has three large peaks and again has low sparsity, but the peak at the natural frequency, 4 Hz, which is the largest in the data represented by the original input digital signal x before the compression, has been decompressed still as the largest peak even after the decompression in contrast to FIG. 13 , and thus it is understood that when compression using the extracted observation matrix ⁇ a is executed, the decompression accuracy is increased.
  • this first embodiment it is understood that, as compared with the conventional compressive sensing technique limited to the case where the sparsity is high, the application range is widened. That is, for use requiring accurate decompression of a specific frequency range around a natural frequency like in health monitoring of a structure, this first embodiment is preferably applied thereto.
  • the power spectral density of each peak has become smaller than that in FIG. 14( a ) .
  • the value of about 3.8 in FIG. 14( a ) has become as small as about 1.4 in FIG. 14( b ) . This is considered to be caused by dispersion of energy, since the waveform is returned and decompressed to a portion at other frequency. Therefore, reproducibility of the power spectral density on the vertical axis is poor.
  • FIG. 15 illustrates this basis transformation matrix ⁇ .
  • the basis transformation matrix ⁇ is found as follows. First, by using the vector x and the vector s of Equation (2), inverse discrete Fourier transform is able to be expressed by the following Equation (4).
  • xi and sn are respectively an i-th element of the vector x and an n-th element of the vector s. Therefore, the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform is as illustrated in FIG. 15 .
  • the compressing unit 11 executes compression by multiplying the input digital signal x by the extracted observation matrix ⁇ a, but the compressing unit 11 of this second embodiment first executes fast Walsh-Hadamard transform, and wirelessly transmits a portion corresponding to a specific frequency portion picked out from the converted digital signal as the compressed digital signal d.
  • FIG. 16 is a block diagram illustrating a configuration of the compressing unit 11 of a transmitting and receiving system, which is the second embodiment.
  • This compressing unit 11 has a fast Walsh-Hadamard transform operation unit 31 and a specific frequency component extracting unit 32 .
  • the fast Walsh-Hadamard transform operation unit 31 executes fast Walsh-Hadamard transform of an input digital signal x.
  • Fast Walsh-Hadamard transform is a process of executing arithmetic processing of a Walsh function with a small number of operations.
  • butterfly operations that are the same as those of fast Fourier transform (FFT) are executed. Therefore, in this second embodiment, by the specific frequency component extracting unit 32 thereafter picking out a portion corresponding to a specific frequency component from a converted digital signal that has been subjected to fast Walsh-Hadamard transform, completely the same result as that in the case where the compression is executed with the extracted observation matrix ⁇ a corresponding to the Walsh function described in the first embodiment is obtained with a small number of operations.
  • FIG. 17 is a block diagram illustrating a configuration of the decompressing unit 22 of the transmitting and receiving system, which is the second embodiment.
  • the specific frequency component extracting unit 32 of the compressing unit 11 outputs the extracted specific frequency component as it is without rearranging its frequency order. Therefore, in the decompressing unit 22 of the second embodiment, a rearranging unit 41 is provided upstream of a decompression operation unit 42 having the same function as the decompressing unit 22 of the first embodiment.
  • the rearranging unit 41 then rearranges the input compressed digital signal d in the frequency order of the Walsh function and outputs the rearranged compressed digital signal d to the decompression operation unit 42 .
  • FIG. 18 illustrates a signal flow of fast Walsh-Hadamard transform algorithm.
  • fast Walsh-Hadamard transform algorithm in the case of the 2 3 -th order is illustrated and the number N of data of the input digital signal x equals 8.
  • the leftmost column represents this input digital signal x (X1, X2, X3, X4, X5, X6, X7, and X8).
  • data of the leftmost column are divided into two groups, (X1, X2, X3, and X4) and (X5, X6, X7, and X8).
  • Addition and subtraction between the head data, X1 and X5, the second data, X2 and X6, the third data, X3 and X7, and the fourth data X4 and X8, of these groups are executed to generate the data of the second column.
  • the data of the second column are further divided into two such that the data are divided into four groups, each group being formed of two data.
  • addition and subtraction are executed in order from between the head datum of the first group and the head datum of the second group, and so on, to generate data of the third column.
  • the data of the third column are further divided into two to obtain eight data, each datum being independent, and addition and subtraction are executed in order from the head datum and the second datum, the third datum and the fourth datum, and so on, to generate data of the fourth column, which are output data. That is, by executing butterfly operations of fast Walsh-Hadamard transform with respect to the input digital signal x (X1 to X8), a converted digital signal t (T1 to T8) is output.
  • FIG. 19 illustrates a specific example of fast Walsh-Hadamard transform.
  • the course of butterfly operations for three-stage addition and subtraction is specifically illustrated, and it is understood that 4, 2, 0, ⁇ 2, 0, 2, 0, and 2 are obtained as the final output.
  • the specific frequency component extracting unit 32 then extracts only a portion corresponding to a specific frequency domain from a result of the operations of fast Walsh-Hadamard transform to realize data compression.
  • FIG. 20 is an explanatory diagram schematically illustrating an extraction process by the specific frequency component extracting unit 32 .
  • FIG. 20 illustrates a case of the 2 3 -th order as an example.
  • the matrix on the right in the figure ( FIG. 20( b ) ) illustrates a Hadamard matrix equivalent to fast Walsh-Hadamard transform.
  • the matrix on the left in the figure ( FIG. 20( a ) ) illustrates a Walsh function corresponding thereto.
  • the arrows between FIG. 20( a ) and FIG. 20( b ) illustrate correspondence between the respective rows.
  • FIG. 20( a ) The second to fifth rows surrounded by a rectangle in FIG. 20( a ) are rows corresponding to a specific frequency domain desired to be extracted. It is understood that rows of the matrix of FIG. 20( b ) corresponding to these rows are the 3rd, 4th, 5th, and 7th rows.
  • FIG. 21 is a diagram illustrating an example of extraction data specifying this specific frequency desired to be extracted. In the extraction data illustrated in FIG. 21 , the 3rd, 4th, 5th, and 7th elements are made “1” to indicate the ordering of elements desired to be extracted, and the other elements are made “0” to indicate the ordering of elements not to be extracted.
  • the specific frequency component extracting unit 32 extracts only a specific frequency domain including a natural frequency, for example, by holding the extraction data illustrated in FIG. 20 beforehand. By executing this extraction of the specific frequency component by the specific frequency component extracting unit 32 , the compressing unit 11 is able to output the input digital signal x as the compressed digital signal d that has been compressed.
  • the natural frequency of a structure is able to be identified by measuring it beforehand, and even if the natural frequency changes due to damage or the like of the structure, the amount of that change is limited, and thus, the specific frequency domain desired to be extracted is able to be held beforehand as the extraction data, the specific frequency domain may be a small domain, and data are able to be compressed widely.
  • the rearranging unit 41 of the decompressing unit 22 executes a process of rearranging the compressed digital signal d extracted with the extraction data of FIG. 21 , in the original order of the Walsh function.
  • the matrix of FIG. 20( b ) illustrates the Hadamard transform matrix that has been subjected to fast Walsh-Hadamard transform
  • the rows surrounded by broken-lined circles therein are the rows corresponding to the extracted specific frequency domain
  • the arrows in the middle each indicate which one of the area surrounded by the broken-lined rectangle corresponding to the specific frequency of the left matrix representing the Walsh function each of these rows corresponds to.
  • the uppermost one of the portion surrounded by the broken-lined circles in the right matrix corresponds to the third one of the portion surrounded by the broken-lined rectangle in the left matrix, the second one of the right to the fourth one of the left, the third one of the right to the first one of the left, and the fourth one of the right to the second one of the left.
  • the rearranging unit 41 holds rearrangement data as illustrated in FIG. 22 , and, based on the rearrangement data, rearranges the compressed digital signal d in the frequency order of the Walsh function.
  • the rearrangement data illustrated in FIG. 22 are “3, 4, 1, 2”, and these values indicate that the first one of the input compressed digital signal corresponds to the third one of the original Walsh function, the second one to the fourth one, the third one to the first one, and the fourth one to the second one.
  • the decompression operation unit 42 executes the same process as the decompressing unit 22 of the first embodiment. That is, the decompression operation unit 42 is able to output the decompressed digital signal x′ by executing data decompression by L1-norm minimization or the like by use of the extracted observation matrix ⁇ a and the basis transformation matrix ⁇ with respect to the rearranged data, similarly to the first embodiment. If the decompression process using the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform is executed, even more accurate decompression is achieved.
  • the fast Walsh-Hadamard transform operation unit 31 of the compressing unit 11 executes fast Walsh-Hadamard transform of the input digital signal x (Step S 301 ).
  • the specific frequency component extracting unit 32 generates the compressed digital signal d by extracting a specific frequency component from the converted digital signal t, which has been subjected to fast Walsh-Hadamard transform (Step S 302 ).
  • the transmitting unit 13 then wirelessly transmits this compressed digital signal d (Step S 303 ) and ends this process.
  • the receiving unit 21 receives the compressed digital signal d (Step S 401 ). Thereafter, the rearranging unit 41 rearranges this compressed digital signal d in the frequency order of the Walsh function (Step S 402 ). Thereafter, the decompression operation unit 42 generates the decompressed digital signal x′ by using the extracted observation matrix ⁇ a, which is the observation matrix corresponding to the Walsh function of the specific frequency component, and the basis transformation matrix ⁇ corresponding to inverse discrete Fourier transform (Step S 403 ), and ends this process.
  • the rearranging unit 41 is provided on the decompressing unit 22 side in order to reduce the processing of the compressing unit 11 installed on the transmitting device 1 side as much as possible to lower the power consumption at the transmitting device 1 side. Even if the rearranging unit 41 is provided in the decompressing unit 22 , at the receiving device 2 side of the wireless sensing system or the like, sufficient power supply is able to be received in general. Of course, the rearranging unit 41 may be provided in the compressing unit 11 at the transmitting device 1 side.
  • the extracted observation matrix ⁇ a of M rows and N columns needs to be held on the memory, and the required memory capacity corresponds to about M ⁇ N.
  • the approximate required memory capacity corresponds to N memories storing the digital signal x and N memories for data for extracting the specific frequency component, requiring only a total of 2 ⁇ N memories.
  • M>>2 as compared to the first embodiment, the required memory capacity is able to be reduced largely, and the transmitting device 1 side, such as the wireless sensor node, is able to be designed to consume even less power.
  • this third embodiment the compression process and decompression process described in the first embodiment that achieve accurate decompression even if the sparsity is low, and the conventional compression process and decompression process that achieve accurate decompression when the sparsity is high, are made to be able to be switched over therebetween.
  • FIG. 25 is a block diagram illustrating a schematic configuration of a transmitting and receiving system, which is the third embodiment. It is different from the transmitting and receiving system described in the first embodiment in that a compressing unit 110 corresponding to the compressing unit 11 has a first compressing unit 111 , a second compressing unit 112 , and a transmission side switch over unit 113 .
  • the transmission side switch over unit 113 causes a compression process with respect to an input digital signal x to be processed by switching over between a compression process by the first compressing unit 111 and a compression process by the second compressing unit 112 .
  • a decompressing unit 120 corresponding to the decompressing unit 22 has a first decompressing unit 121 , a second decompressing unit 122 , and a reception side switch over unit 123 .
  • the reception side switch over unit 123 causes a decompression process with respect to an input compressed digital signal d to be processed by switching over between a decompression process by the first decompressing unit 121 and a decompression process by the second decompressing unit 122 .
  • the first compressing unit 111 corresponds to the compressing unit 11 of the first embodiment. Further, the first decompressing unit 121 corresponds to the decompressing unit 22 of the first embodiment.
  • the second compressing unit 112 executes the compression process of the input digital signal x by using a random matrix as the observation matrix ⁇ (hereinafter, referred to as the random observation matrix ⁇ ). Furthermore, the second decompressing unit 122 executes the decompression process by using the random observation matrix ⁇ .
  • a receiving device 102 corresponding to the receiving device 2 has a switch over instruction unit 124 .
  • the switch over instruction unit 124 sends out a switch over instruction signal to the transmission side switch over unit 113 and sends out the switch over instruction signal to the reception side switch over unit 123 , via a transmitting unit 125 provided in the receiving device 102 and a receiving unit 115 provided in a transmitting device 101 .
  • This switch over instruction signal is associated with execution of a switch over instruction for the decompression process by the first decompressing unit 121 if the switch over instruction signal indicates a switch over instruction for the compression process by the first compressing unit 111 .
  • the switch over instruction signal is associated with execution of a switch over instruction for the decompression process by the second decompressing unit 122 if the switch over instruction signal indicates a switch over instruction for the compression process by the second compressing unit 112 .
  • FIG. 26 is a block diagram illustrating a detailed configuration of the compressing unit 110 .
  • the compressing unit 110 has switches SW 11 and SW 12 respectively provided upstream of and downstream from the first compressing unit 111 and the second compressing unit 112 that are arranged in parallel with each other.
  • the switches SW 11 and SW 12 form the transmission side switch over unit 113 .
  • the switches SW 11 and SW 12 execute, based on the switch over instruction signal input via the receiving unit 115 , switch over between connection to the first compressing unit 111 and connection to the second compressing unit 112 , in synchronization therewith.
  • FIG. 27 is a block diagram illustrating a detailed configuration of the decompressing unit 120 .
  • the decompressing unit 120 has switches SW 21 and SW 22 respectively provided upstream of and downstream from the first decompressing unit 121 and the second decompressing unit 122 that are arranged in parallel with each other.
  • the switches SW 21 and SW 22 form the reception side switch over unit 123 .
  • the switches SW 21 and SW 22 execute, based on the switch over instruction signal input via the switch over instruction unit 124 , switch over between connection to the first decompressing unit 121 and connection to the second decompressing unit 122 , in synchronization therewith.
  • the switch over instruction unit 124 functions as an operation input unit, and is able to execute, based on the decompressed state of the decompressed digital signal x′, a switch over instruction between the compression and decompression processes by the first compressing unit 111 and the first decompressing unit 121 , and the compression and decompression processes by the second compressing unit 112 and the second decompressing unit 122 .
  • the transmitting device 1 determines whether or not a switch over instruction signal instructing a first compression process has been input (Step S 501 ). If the switch over instruction signal instructs the first compression process (Step S 501 : Yes), the switches SW 11 and SW 12 are connected to the first compressing unit 111 and the compression process by the first compressing unit 111 is executed (Step S 502 ).
  • Step S 501 if the switch over instruction signal does not instruct the first compression process (Step S 501 : No), the switches SW 11 and SW 12 are connected to the second compressing unit 112 , and the compression process by the second compressing unit 112 is executed (Step S 503 ). Thereafter, the transmitting unit 13 wirelessly transmits the compressed digital signal d output from the compressing unit 110 (Step S 504 ) and ends this process.
  • the above described process is processed repeatedly.
  • the receiving device 2 determines whether or not the switch over instruction signal instructing the first compression process has been input (Step S 601 ). If the switch over instruction signal instructs the first compression process (Step S 601 : Yes), the switches SW 21 and SW 22 are connected to the first decompressing unit 121 and the decompression process by the first decompressing unit 121 is executed (Step S 602 ). On the contrary, if the switch over instruction signal does not instruct the first compression process (Step S 601 : No), the switches SW 21 and SW 22 are connected to the second decompressing unit 122 and the decompression process by the second decompressing unit 122 is executed (Step S 603 ). The above described process is processed repeatedly.
  • the compression and decompression processes using the extracted observation matrix ⁇ a corresponding to the Walsh function are executed, and accurate decompression is achieved by making limitation to the specific frequency component even if the input digital signal x has low sparsity.
  • the first embodiment has limitation on the frequency domain to be decompressed.
  • the conventional compression and decompression processes using the random observation matrix ⁇ decompression of the entire frequency domain is possible, but unless the sparsity is high, the decompression error becomes large.
  • the sparsity of the input digital signal x is able to be determined to be low by investigating characteristics of the decompressed digital signal x′, switch over to the compression and decompression processes by the first compressing unit 111 and the first decompressing unit 121 by use of the extracted observation matrix ⁇ a corresponding to the Walsh function is executed. Further, if the sparsity of the input digital signal x is able to be determined to be high, switch over to the compression and decompression processes by the second compressing unit 112 and the second decompressing unit 122 by use of the random observation matrix ⁇ is executed.
  • the first compressing unit 111 of the third embodiment has been replaced with the compressing unit 11 of the second embodiment, and the first decompressing unit 121 of the third embodiment 3 has been replaced with the decompressing unit 22 of the second embodiment. Therefore, the first compressing unit 111 has a fast Walsh-Hadamard transform operation unit 111 a corresponding to the fast Walsh-Hadamard transform operation unit 31 , and a specific frequency component extracting unit 111 b corresponding to the specific frequency component extracting unit 32 .
  • the first decompressing unit 121 has a rearranging unit 121 a corresponding to the rearranging unit 41 and a decompression operation unit 121 b corresponding to the decompression operation unit 42 .
  • the compressing unit since the compressing unit generates and outputs the compressed digital signal compressed by the conversion of the input digital signal using the Walsh function and the extraction of the specific frequency component, even if the original input digital signal has low sparsity, accurate decompression with respect to the specific frequency component is able to be executed.
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